Algebra 1 Unit 3: Systems of Equations s1

AFM Unit 4 Piecewise-defined Functions Goal 2.02

Enduring understanding (Big Idea): SUGGESTED TIME: 5 DAYS Students will understand that piecewise-defined functions are used to model situations when a single function will not work. (Ex. Income Taxes: graduated vs. flat rate) Essential Questions: •What real-life situations can be represented by piecewise functions? • What are the characteristics of piecewise functions?

BY THE END OF THIS UNIT: Students will know… Students will be able to… • Evaluate piecewise-defined functions for particular domain values • That piecewise functions behave differently for different domain • Graph piecewise functions values • Identify real-world situations that can be represented with piecewise functions. • Identify piecewise functions as continuous or discontinuous and increasing Vocabulary: graph, independent, dependent, domain, range, or decreasing minimum, maximum, increasing, decreasing, Global versus Local behavior, continuous, discrete, system of Equations, solve equations - justifying steps

Unit Resources Mathematical Practices in Focus: Learning Task: Indicator 2.02-C 1-Make sense of problems and persevere in solving them Performance Task: See UNC Module 5 3-Construct viable arguments and critique the reasoning of others Project: Piecewise Logo Project (Resource Folder) 4-Model with mathematics Unit Review Game: 6-Attend to precision MathForward: 7-Look for and make use of structure Graph it in pieces

Successive pages contain an unpacking of the standards contained in the unit. Standards are listed in alphabetical and numerical order not suggested teaching order. Teachers must order the standards to form a reasonable unit for instructional purposes AFM Unit 4 Piecewise-defined Functions Goal 2.02

CORE CONTENT Cluster Title: N/A Standard NCCOS 2.02 Use piecewise-defined functions to model and solve problems; justify results. A) Solve using tables, graphs, and algebraic properties. B) Interpret the constants, coefficients, and bases in the context of the problem. Concepts and Skills to Master • Solve using tables, graphs, and algebraic properties. • Interpret the constants, coefficients, and bases in the context of the problem. SUPPORTS FOR TEACHERS Critical Background Knowledge: • Evaluate functions • Graph inequalities • Understand relevant domain • Understand how to describe intervals Academic Vocabulary Domain, range, minimum, maximum, increasing, decreasing, global vs. local, continuous, discrete Suggested Instructional Strategies Resources  Textbook Correlation: • Review of Geometry If-Then statements Textbook-Pre-calculus-Glencoe (PG) • (AMC) p.132 Crystallography Example Chapter 1, Section 1-1, p.8 Ex. 6 Textbook-Advanced Mathematical Concepts (AMC) pp.45-48, 60-61, 132, 161, 170, 196, 199  UNC Module 5  Lessons: http://www.dlt.ncssm.edu/AFM/bygoal.htm  Lessons: http://www.learnnc.org/scos/2004-MAT/ADFM/01/  http://www.glencoe.com/sec/math/precalculus/amc_04/self_check_quiz/  MindSet –  Study Island

Sample Formative Assessment Tasks Skill-based task Problem Task (PG) p.10 #52 2.02-D Indicator

Teacher Created Argumentation Tasks (W1-MP3&6): Variation of example 2 in Module 5 - 5.7: Pair up students, each student draws a graph of time vs. speed depicting their activities for the day. The students then swap graphs and write scenarios for their partners’ graph. The students then critique one another’s scenarios. Do you agree with the scenario? Why or why not?